physics of the tackle

In this preliminary analysis we will consider the tackle according to:
1 Relative direction of ball carrier and tackler (front, side or rear)
2 Height of tackle (legs, Mid below com, mid above com)

For the first stage the ball carrier is assumed to run upright and to behave as a rigid body during the tackle (flexibility and the changes it causes will be considered later). The tackler will be assumed to strike the carrier at a single point and grasps the ball carrier so that they behave as a single object after the tackle. The players are also assumed to stop running on impact.

A) Tackle from in front on the lower legs. (It is difficult to make this tackle).

Torque and angular acceleration: The force exerted on the point of contact makes a small angle with the horizontal and is a relatively large distance from the centre of mass of the carrier thus exerting a large torque about the centre of mass. Relative to the centre of mass of the carrier, therefore, there will be a large angular acceleration of the feet backward, that is, the carrier will rotate forward about the feet. The higher the tackle is made, the smaller the horizontal component of the force and the shorter the distance to the centre of mass.
Once the centre of mass has moved forward of the base, or because the carrier can no longer drive with the feet and loses dynamic equilibrium, the weight of the ball carrier will exert a torque about the point of contact or feet and the rotation in the forward sense will accelerate at an increasing rate as the CofM moves forward. The carrier at this stage can no longer recover even if released and the tackler is able to release and recover a standing position more quickly.
Angular momentum: Viewed from any fixed point or axis, a moving mass has angular momentum about that axis. This angular momentum is conserved if any force exerted on the mass is acting along the line joining the mass to the axis. Viewed relative to the transverse and frontal axes, once the tackler has grasped the carrier, the force between them becomes tension in the legs, that is, along the line from tackler to centre of mass. The angular momentum of the running mass is then converted into rotation of the carrier about the tackler. The moving mass may be either the ball carrier approaching the tackler or vice versa or a combination of the two. In terms of the rotation caused the end result is the same and the ball carrier falls forward toward the ground.
Viewed about the vertical axis, a safe tackle will tend to exert a small eccentric torque causing rotation of the ball carrier towards his back and leaving the tackler face down ready to recover his feet quickly. While the torque is small, the moment of inertia about this axis is also small allowing for a large angular displacement.

Impulse and momentum: At the point of impact, the force exerted by the tackler on the carrier and the force exerted by the carrier on the tackler are equal and opposite (Newton’s third law) and the time of contact is the same for each. Assuming the tackle is taken as an isolated event, the impulse (F.t) will give rise to an equal and opposite change in momentum for each body. E.g. if the tackler is stationary and the carrier is moving the carrier will be slowed in the impact and the tackler will be carried backwards. On the other hand a fast approaching tackler can drive the ball carrier backward without using drive from the ground reaction. These motions will all be subsequently altered by ground contact forces. Since the change in momentum of each player is the same, the more massive player will change velocity by a smaller amount giving dominance to the larger player in the tackle. (The smaller player can of course accelerate more rapidly to avoid the tackle).

Energy and work:

Since energy depends on the square of the speed, a higher speed player will have much more energy than a lower speed or stationary player. In a tackle between two players moving at different speeds the final speed will be between the initial speeds of the players so that the faster must lose more energy than the slower gains. In general the tackler in slowing the carrier down, therefore, does more work on the carrier than vice versa.

B) Tackle from side on legs. (common tackle on and by outside backs)

This time the force exerted by the tackler has a lateral component as well as a component backward relative to the motion of the centre of mass. Thus the angular momentum of the carrier is both forward and across the tackler so that the carrier will rotate about both the transverse and frontal axes, and will fall forward and to one side. The loss of drive from the feet and the tackling force will result in a net torque from the weight of the carrier and the tackle force causing the same accelerated rotation as before.
The sum of the momenta of the two players will now have a lateral component so that they will together move towards the side away from the point of contact subject again to ground forces.

In both of the above tackles, the rotation of the ball carrier about the centre of mass may be sufficient that the feet are carried off the ground for a substantial period while the centre of mass is falling under gravity. If the tackler is able to retain his feet and thus continue the drive around one of the horizontal axes it is possible that the ball carrier will become inverted and the tackle will become a spear tackle. The tackler must, therefore, ensure that the drive stops and tackle is completed before the ball carrier is moved past the horizontal.

C) Tackle from behind on legs. (catching a slower player who has broken through).

Normally the relative velocity of the tackler and the ball carrier will be small so that the tackle depends on removing the forward drive from the feet by wrapping the legs and applying a relatively smaller backward frictional force on the tackler once the tackle has been made. As a consequence a net torque is applied forward relative to the feet (or backward below the cofm) so that the tackled player falls forward. It may be sufficient merely to prevent the drive momentarily as in an ankle tap since the inertia of the centre of mass will be ahead of the player’s base and he will be unstable. Without the forward component of the ground reaction force, the ball carrier will rotate forward to a position from which it is difficult if not impossible to recover equilibrium. In any case to recover equilibrium will require the leading foot to reach ahead of the body giving a braking reaction and slowing the player down. Occasionally the relative velocity may be large, for example, when a chaser meets a stationary catcher who is facing towards their own end of the field. In this situation the feet of the carrier are carried forward relative to the com and the net torque rotates the player backward to land on their back.

D) Tackle front on, near or below centre of mass (midriff).
This is the classic tackle taught to beginners and uses the “cheek to cheek” contact.

Torque and angular acceleration: The force exerted by the tackler who has adopted a low position with a straight back is now angled upwards at an intermediate angle to the horizontal and is directed close to the com so that the moment of the force about the com is small. If the ball carrier is relatively upright and the reaction of the ground has only a small horizontal component, the net torque on the tackler will be small. The low body position of the tackler means that the impact force will exert a substantial torque about the feet of the tackler causing the tackler to rotate backwards and upwards about the feet. If the tackler has a firm grip on the ball carrier this will cause the carrier to be lifted as the angle of the tackler to the horizontal increases.
The tackler will endeavour to grip the carrier firmly while allowing the grip to fall down the legs preventing the carrier from continuing to run. The high contact and descending grip has the advantage of avoiding the need to try to grip the moving knees yet allowing them to be held in completing the tackle.
To enable the tackler to avoid neck damage it is normal to aim the head to one side and engage the ball carrier with the shoulder (the cheek to cheek position). In this position the force of the tackler on the carrier is eccentric to the vertical axis of the carrier exerting a small net torque about the vertical axis and causing rotation of the carrier out of the direction of travel. This will tend to place the tackler on top and in the best position to recover his feet and secure possession. To facilitate this the tackler will move into a tuck position which reduces the moment of inertia allowing quicker rotation from the prone position at the end of the tackle to an upright position and placing the body in a strong crouch.
A ball carrier who anticipates the rotation in the tackle by commencing rotation before contact can alter the point of contact to his advantage and make use of the additional torque to spin out of the tackle


Momentum and Impulse:

Since the line of action of the tackling force is through or close to the centre of mass of the carrier the collision at the instant of the tackle can be considered as a pure linear collision with conservation of momentum. Thus a stationary or slow moving tackler will be driven backward in the tackle by a fast moving carrier at a speed determined by the original velocity and the masses of the players.
If the tackler has a greater mass and speed than the carrier, the carrier will be driven backward.

For equal masses:
the stationary tackler and the moving carrier will move at half the original speed and the impulse on each will be half the momentum.
Tackler and carrier at equal speeds will come to a halt and the impulse on each will be equal to the momentum of each before contact.
Moving tackler and stationary carrier is the reverse of the original case and the impulse is again half.
Other combinations of velocity and mass will give intermediate values of impulse.
The time of impact is determined by the distance over which the impact takes place so that a tackle aimed at a bony body part, e.g. hip, will take less time than one aimed at a softer area, e.g. midriff and the net force at the point of contact will accordingly be larger. The use of padding, as allowed by the laws, will not affect the overall impulse, but will give some increase in time and thus decrease in force with the aim of protecting the bony parts of the tackler e.g. the collar bone.

Tackle from the side or behind: Since there is no backward component in either case, the carrier will continue to move forward taking the tackler with them. For equal masses and speeds the pair will move diagonally at about two thirds of the speed and each will experience an impulse of half the original momentum. From behind the impulse will decrease, reaching zero when the speeds are equal. In the case of the side on tackle, there will still be some torque enabling the tackler to turn the carrier and again gain a dominant position on the ground.

Tackle above centre of mass
In front

Since the point of contact is high, the tackler must be relatively upright and the force exerted by the tackler from the ground will have only a small horizontal component. The moment arm is also relatively small as the point of contact cannot be above shoulder level. Accordingly the torque is relatively small about the centre of mass. If the carrier is, however, making good ground contact and/or is driving through the feet. The force of the tackle and the ground contact will act as a force couple giving a some torque in the backward sense about the feet forcing the carrier to rotate backward with the tackler on top. Often, however, the tackler will use his own weight to increase the inertia of the carrier’s upper body causing him to fall forward. In this case the tackler will need to twist during impact to gain the dominant position and will require a wide base to give sufficient torque by ground reaction.

From side

The results are similar to the previous case except that the torque is now both to the opposite side from the tackler and backward (from the ground contact). This will make it easier for the tackler to turn the carrier and gain dominance.


From behind

Now the tackler can exert almost no torque in the contact and must rely on ground contact forces after initiating the tackle to bring it to completion. It is not unknown for the ball carrier to ‘carry’ the tackler for a considerable distance in this position since a smaller tackler is unable to exert large forces on the ground while gripping the upper body of the carrier.

Additional factors affecting the tackle

The majority of the discussion above assumes that the ball carrier is a rigid upright body in contact with the ground only in so far as is necessary for running at normal speeds. The body is of course flexible with major relevant joints at the hip and the knee. Also by adjusting orientation during the tackle phase it is possible to vary the ground contact forces and thus the reaction thereto and the thrust acting on the ball carrier. The ball carrier has the ability to modify the point or direction of impact by changing the body orientation immediately before impact.
The tackler has been assumed to be a form of projectile exerting a force on the tackler only because of their relative motion at impact. By using the reaction to ground contact forces the tackler can adjust the speed of impact and can change the direction of the force by altering body orientation immediately before impact. The tackler can also extend the effect of the tackle after impact by maintaining leg drive during and after impact. They may also exert torsional forces on their own body and on the carrier to cause rotation during the tackle.

The ball carrier

By bending at the hips and using a bent knee running action the ball carrier will lower the centre of mass and reduce the distances of the extremities from the centre of mass. This will increase the stability of the carrier and will reduce the moment arm of the force exerted by the tackler. These will reduce the chance that the carrier will be rotated in the tackle. On the other hand, if the tackler is able to overbalance the carrier the smaller moment of inertia in the crouched position may result in a quicker grounding. The higher knee action in this style of running makes it more difficult for the tackler to grasp the legs and the ball carrier may be able to break the tackle by driving through, that is, to continue to run vigorously so that the tackler cannot complete the wrap.

The ball carrier can disrupt the tackle if the tackler is approaching from an arc to the side by leaning towards the tackler with the upper body so that the legs are angled away from the tackler. The weight of the carrier will, of course, exert a torque tending to make the carrier fall toward the tackler which must be counteracted by an inward (centripetal) drive through the legs, or by a fend exerted against the tackler. The tackler thus finds it more difficult to reach the target and the tackle is easier to break. To reach the ball carrier, the tackler must adopt a less stable low upper body or a forward lean and the downward fend in this case will increase the forward torque on the tackler who will then rotate or fall forward.

When tackled from a forward side arc, the tackler exerts an eccentric force at impact, causing a torque about a vertical axis through the carrier. By initiating rotation in the same sense the carrier can enhance the effect of that torque, moving the target area away from the point of impact into the weaker region of the tackler’s arms and thus rolling out of the tackle using the small moment of inertia about the vertical axis to aid his rotation. Lifting the arms and ball above the tackle not only frees the ball for a subsequent pass, it may also cause a reduction in moment of inertia for the ball carrier accelerating the spin out of the tackle. If this is not successful however, it has exposed a vulnerable area of the carrier to the tackler.

Just before impact in the tackle, the carrier can step forward into contact, (the ‘power step’ increasing the momentum of the carrier at impact and rotating the body to present the stronger side aspect to the tackler. This will also drop the centre of mass, and widen the base of the carrier at the time of impact so the carrier is more stable and thus less likely to be taken to ground in the tackle. The carrier also to some extent gains control of the height of impact and can exert sufficient torque on the tackler to initiate backward rotation. If the step is away from the core of the tackler, the impact will be on the arm which is weaker than the shoulder, it will exert a large torque on the tackler so that the momentum of the ball carrier will now be directed towards the hands of the tackler making the grip more difficult to maintain, ie, breaking the tackle.

The tackler

The tackler will normally maintain full contact with the ground and leaning forward to give a large horizontal component to any force on impact. This is most easily obtained if the tackler is moving so that the driving force from the ground contact is forward to counteract the torque of the weight when the centre of mass is ahead of the feet.
During impact the ground contact will effectively increase the mass and hence momentum of the tackler. If the tackler’s body remained completely rigid, the carrier would be stopped dead or driven back at the speed of the tackler. This is of course not possible if the tackler is moving or has flexed joints, but is approached if the tackler ensures that ground contact is maintained in the tackle and that the legs drive through the tackle. In this case the tackler may take shorter strides before and during contact to maintain the driving force. A forward lean will also cause the tackler to pivot about the tackler’s feet as the angular momentum of the carrier about the tackler is transferred to the combined system, carrying the carrier upward from the ground. At this point the tackler is in ground contact and can rotate the carrier so that the tackler lands on top and the carrier is on his back putting the tackler in control. Continued drive by the tackler in a head on tackle can stop the carrier and drive them backward without rotation to land on their back, tackler on top.
In any tackle other than from behind, the tackler aims to ensure that their head is behind the carrier or at least on the side from which the tackler is approaching so that the head is not struck in the tackle. To achieve this, the tackler attempts to stay on the side of the tackler on which the contact will be made so that any change in direction can be allowed for. It will also tend to put the tackler on top after it is complete.

A substantial proportion of tackles in a game are not clean one-on-one challenges but are low speed upright mauls in which neither party is dominant.